A man can complete a task in 7 days but with the help of his son, he can complete it in 4 days. In how many days can his son complete it alone?

Correct option is B

Given:

A man can complete the task in 7 days.

With the help of his son, they can complete the task in 4 days.

We need to find how many days the son alone can complete the task.

Solution:

Work rate of man =$$\frac{1}{7}$$​

Combined work rate =$$\frac{1}{4}$$​

The combined work rate is the sum of the individual work rates of the man and his son:

Combined work rate = Work rate of man + Work rate of son

​$$\frac{1}{4} = \frac{1}{7} + \frac{1}{\text{time taken by son}}$$​

Let the time taken by the son be x. Thus, we have:

​$$\frac{1}{4} = \frac{1}{7} + \frac{1}{x}$$​​

​$$\frac{1}{x} = \frac{1}{4} - \frac{1}{7}$$​​

​$$\frac{1}{x}= \frac{1}{4} - \frac{1}{7} = \frac{3}{28}$$ 

​$$x = \frac{28}{3}$$ = 9$$\frac13$$ days

The son can complete the task alone in $$9\frac 13$$ days.

Alternate Method:

Efficiency of Son = 7 - 4 = 3

Son complete the work = $$\frac{28}{3}=9\frac 13$$ days​